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- W2897523366 abstract "We consider families of linear systems that are defined by matrix pairs $big( A(theta),B(theta) big)$ which depending on a parameter $theta$ that is varying over a compact set in the plane. The focus of this paper is on the task of steering a family of initial states $x_0(theta)$ in finite time arbitrarily close to a given family of desired terminal states $x^*(theta)$ via a parameter-independent open-loop control input. In this case the pair $big( A(theta),B(theta) big)$ is called ensemble reachable. Using well-known characterizations of approximate controllability for systems in Banach spaces, ensemble reachability of $big( A(theta),B(theta) big)$ is equivalent to an infinite-dimensional extension of the Kalman rank condition. In this paper we investigate structural properties and prove a decomposition theorem according to the spectra of the matrices $A(theta)$. Based on this results together with results from complex approximation and functional analysis we show necessary and sufficient conditions in terms of $big( A(theta),B(theta) big)$ for ensemble reachability for families of linear systems $big( A(theta),B(theta) big)$ defined on the Banach spaces of continuous functions and $L^q$-functions. The paper also presents results on output ensemble reachability for families $big( A(theta),B(theta),C(theta) big)$ of parameter-dependent linear systems." @default.
- W2897523366 created "2018-10-26" @default.
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- W2897523366 date "2018-10-22" @default.
- W2897523366 modified "2023-09-27" @default.
- W2897523366 title "Uniform and $L^q$-Ensemble Reachability of Parameter-dependent Linear Systems" @default.
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